Abstract
AbstractWe focus on a very general problem in the theory of dynamic systems, namely that of studying measure differential inclusions with varying measures. The multifunction on the right hand side has compact non-necessarily convex values in a real Euclidean space and satisfies bounded variation hypotheses with respect to the Pompeiu excess (and not to the Hausdorff-Pompeiu distance, as usually in literature). This is possible due to the use of interesting selection principles for excess bounded variation set-valued mappings. Conditions for the minimization of a generic functional with respect to a family of measures generated by equiregulated left-continuous, nondecreasing functions and to associated solutions of the differential inclusion driven by these measures are deduced, under constraints only on the initial point of the trajectory.
Funder
Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Geometry and Topology,Numerical Analysis,Statistics and Probability,Analysis
Cited by
13 articles.
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